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Math Help - What values f(X) can get ?

  1. #1
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    What values f(X) can get ?

    Hi Guys,

    I try to calculate the values that this function can "get".

    According to my calcs, it's X<=-4 or X>4.
    When I plotted it, I saw that it also gets values between -3 and 2. I don't understand why. Can anyone please show me the calculations that bring to that result ?

    cheers !

    What values f(X) can get ?-fx.jpg
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  2. #2
    MHF Contributor Unknown008's Avatar
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    f(x) = \dfrac{\sqrt{x^2 + 2x - 8}}{\sqrt{x^2 - x - 12}} = \dfrac{\sqrt{(x+4)(x-2)}}{\sqrt{(x+3)(x-4)}}

    So, x cannot be equal to -3 or 4, because there, you have an asymptote.
    At x = -4 and 2, you have f(x) = 0.

    Anything negative is imaginary.

    When you take the intervals, you have -4, -3, 2, 4.

    And trying in values smaller than -4 gives a solution.
    At -4, you have 0.
    Between -4 and -3, you don't have any solution.
    At -3, you get infinity.
    Between -3 and 2, you get solutions.
    At 2, you get 0 again.
    Between 2 and 4 you get no solutions.
    At 4, you get again infinity and beyond that, you get solutions.
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